Question

The angle of elevation of the top of a tower (which is yet incomplete) at a point $120ft$. from its base is ${45}^{\circ }$. How much higher should it be raised, so that the elevation at the same point may become ${60}^{\circ }$?

Answer 1

$AB$ subtends an angle of ${45}^o$ at $P$ where $AP=120$.

$\therefore AB=AP=120$

from isosceles tingle $ABP$

Again $\frac{120+h}{120}=\tan {60}^o=\sqrt{3}$

$\therefore h=120(\sqrt{3}-1)$